Unit #4: Navigating Networks

Lesson 1: Introduction to Networks

Duration: 60 minutes
Level: Curriculum Level 7 (NCEA Level 2)
Subject: Mathematics – Geometry and Measurement
Strand Focus: Relationships in Geometry (Networks)

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Achievement Objectives (NZC Level 7)

• Apply network and graph theory methods in practical contexts.
• Identify, model, and solve problems involving optimisation.
• Communicate mathematical thinking coherently using appropriate representations and strategies.

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Learning Intentions

By the end of this session, students will be able to:

• Define key terms in network theory: nodes, edges, and paths.
• Identify examples of networks in real-life contexts (e.g., transport, internet, electricity).
• Represent simple networks visually.
• Discuss how networks are used for decision-making and problem-solving in real-world scenarios.

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Success Criteria

Students can:

• Accurately define and explain network key terms.
• Draw a labelled diagram showing a real-world network scenario.
• Actively contribute to building a class network diagram.
• Explain how networks impact daily life and future careers.

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Lesson Sequence

1. Mihi / Karakia / Settling In (5 minutes)

• Begin with a brief welcome, karakia, or mindfulness reflection to set a respectful and focused tone.
• Ensure students are ready with paper, pens, or devices if digital work is being used.

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2. Mahi Tāmata – Hook Activity (10 minutes)

Activity: “Find the Fast Track”

• Scenario given on board or screen: “You’re planning a weekend festival for 10,000 people with food trucks, parking areas, and toilets. How do people move around easily?”
• Students work in pairs to sketch their ideas in 5 minutes: What paths would you build? Where would people walk?
• Encourage quick, messy drawings.
• Volunteers briefly share sketches and ideas with class.

Purpose: Activate prior knowledge of pathways and movement; introduces idea of networks through a relatable, real-world context.

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3. Ako – Teacher-led Input (10 minutes)

Content Presentation:
Introduce key definitions with visual examples:

• Node (also called vertex): a point (e.g. intersection, town, computer).
• Edge (also called arc): the connection between nodes (e.g. road, cable).
• Networks: a collection of nodes and edges.
• Explain directed and undirected networks using arrows on the board.
• Introduce weighted networks (e.g. cost, time, distance).

Example NZ-Based Contexts:

• Transport network in Wellington or Auckland.
• Internet infrastructure between towns.
• Irrigation system on a farm.

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4. Interactive Group Activity – "Walk the Network" (15 minutes)

Materials: String, labels, printed town/landmark cards
Instructions:

• Turn the classroom into a physical network!
• Allocate students to be nodes holding cards labelled "School", "Library", "Bakery", etc.
• Use string to represent edges between students (can also hold laminated strips showing time/distance).
• Give travel instructions to pairs: “Get from School to Bakery in the shortest time.”
• Class discusses various paths taken – which is shortest? Is that always the best?

Purpose: Hands-on exploration of networks using bodies and space. Encourages movement, problem-solving, and collaboration.

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5. Whakawhitinga Kōrero – Group Discussion (10 minutes)

Prompt questions:

• Where do we see networks in everyday life in Aotearoa?
• How would you use these ideas in real-world jobs (e.g. urban planning, logistics, computer science)?
• What would happen if a node breaks down in a network?

Teacher records student responses on whiteboard (use a spider diagram or concept map format). Encourage students to use the vocabulary introduced.

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6. Individual Task – Interactive Sketch & Reflect (10 minutes)

Task: Students complete a worksheet or digital slide:

• Draw their own 3-5 node network example from their local environment (e.g. bus routes from home, classroom furniture layout, friend's social media links).
• Label nodes and edges.
• Write a short paragraph (3–4 sentences): "How is this an example of a network? How could I make it more efficient?"

Teacher circulates and supports students using scaffolding questions.

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7. Poroporoaki / Reflection (Post-task Wrap-Up – 5 minutes)

Whole class reflection:

• One thing I learnt...
• One place I can now see networks...
• One question I have...

Teacher notes insights for use in Lesson 2.

Optional: Use sticky notes on the board or a digital padlet for anonymous reflection.

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Assessment for Learning

• Formative, observational assessment during group and individual tasks.
• Review student sketches and written reflections for understanding of network structure.
• Identify students who may need support in Lesson 2 or extension opportunities.

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Differentiation

• Support: Students can pair up for the drawing task; provide a scaffolded worksheet with a word bank or partially completed diagrams.
• Extension: Challenge early finishers to create a weighted network and calculate the shortest route. Option to link this with career pathways in logistics or IT.

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Key Connections and Real-World Relevance

• Curriculum Integration: Links to Digital Technologies (networks), Geography (mapping movement), and Career Pathways (logistics, urban planning).
• Mātauranga Māori: Discuss traditional navigation and how networks of stars, whenua, and people guided journeys across the Pacific.
• Employability Skills Developed:
  • Teamwork (mahi ngātahi)
  • Thinking skills (he hiahia ki te ako)
  • Communication (whitiwhiti kōrero)

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Preparation for Next Lesson

Coming Up: Lesson 2 – Network Representation: Students will learn to analyse and draw different types of network graphs including tree diagrams, cycles, and connected graphs.

Homework / Optional Task:
Students take photos or draw networks they see in their neighbourhood, school, or whānau context (e.g. power lines, furniture layout). Bring to next lesson for warm-up.

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Kia kaha, kaiako! Engaging learners through movement, story, and community – maths with meaning.